Thomas Kerler - Böcker
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2 produkter
2 produkter
Del 1765 - Lecture Notes in Mathematics
Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
Häftad, Engelska, 2001
536 kr
Skickas inom 10-15 vardagar
d + 1-dimensional manifold, whose is a union of d-dimensional boundary disjoint v manifolds and d, a linear : -+ The manifold -Zod V(Md+l) V(Zod) V(Zld). ma- is with the orientation. The axiom in that z0g, Zod opposite gluing [Ati88] requires if we two such d + 1-manifolds a common d-subma- glue together along (closed) fold of in their the linear for the has to be the boundaries, composite compo- map tion of the linear of the individual d + 1-manifolds. maps the of and as in we can state categories functors, [Mac88], Using language axioms as follows: concisely Atiyah's very Definition 0.1.1 A in dimension d is a ([Ati88]). topological quantumfield theory between monoidal functor symmetric categories [Mac881 asfollows: V : --+ k-vect. Cobd+1 finite Here k-vect denotes the whose are dimensional v- category, objects for field tor over a field k, which we assume to be instance, a perfect, spaces The of of characteristic 0. set between two vector is morphisms, simply spaces the set of linear with the usual The has as composition. category Cobd+1 maps manifolds. such closed oriented d-dimensional A between two objects morphism.Zd d oriented d 1-- d-manifolds and is a + 1-cobordism, an + Zod meaning gMd+l = Zd is the d- mensional manifold, Md+l, whose Lj boundary _ZOd of the d-manifolds. consider union two we as joint (Strictly speaking morphisms cobordisms modulo relative Given another or homeomorphisms diffeomorphisms).
Del 1542 - Lecture Notes in Mathematics
Quantum Groups, Quantum Categories and Quantum Field Theory
Häftad, Engelska, 1993
536 kr
Skickas inom 10-15 vardagar
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U_(sl,) for q a primitive root of unity, and a semi-simple quotient thereof, a classification of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum field theory. The reader is expected to be familiar with basic notions and results in algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.